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arXiv · 2004.08822

Shifted inverse curvature flows in hyperbolic space

Xianfeng Wang·Yong Wei·Tailong Zhou
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Abstract

We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces in hyperbolic space expanding by $F^{-p}$ with positive power $p$ for a smooth, symmetric, strictly increasing and $1$-homogeneous curvature function $f$ of the shifted principal curvatures with some concavity properties. We study the maximal existence and asymptotical behavior of the flow for horo-convex hypersurfaces. In particular, for $0<p\leq 1$ we show that the limiting shape of the solution is always round as the maximal existence time is approached. This is in contrast to the asymptotical behavior of the (non-shifted) inverse curvature flow, as Hung and Wang [18] constructed a counterexample to show that the limiting shape of inverse curvature flow in hyperbolic space is not necessarily round.

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Xianfeng Wang, Yong Wei, Tailong Zhou. 2020-04-19. Shifted inverse curvature flows in hyperbolic space. https://doi.org/10.1007/s00526-023-02429-2

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